Characterization of the Geomagnetic Field and Its Dynamic Environment
Using Data from Space-Based Magnetometers

Editorial Board (July 2022)
Editor-in-Chief
Takeshi Sagiya, Nagoya University, Japan

Vice Editors-in-Chief
Masahito Nosé, Nagoya University, Japan

Aitaro Kato, University of Tokyo, Japan

Editors
Koki Aizawa
Hideo Aochi
Pascal Audet
Kiyoshi Baba
Joseph B.H. Baker
Nanan Balan
Stephan Christoph Buchert
Sonia Calvari
Xiaowei ChenPeter Chi
Harold C. Connolly Jr
Phil Cummins
Hao Dong
Guangyu Fu
Hidenori Genda
Aditya Gusman
Tomasz Hadaś
Stuart Henrys
James Hickey
Hauke Hussmann

Mie Ichihara
Hidekatsu Jin
Art Jolly
Shunichi Kamata
Nobuki Kame
Katsuya Kaneko
Ikuo Katayama
Yoko Kebukawa
Kunihiro Keika
Kostas Konstantinou
Alexey Kuvshinov
Juanjo Ledo
Koji Matsuo
Yasunobu Miyoshi
Atsuko Namiki
Yasuhito Narita
Kazunari Nawa
Kiwamu Nishida
Hiroyo Ohya
Duggirala Pallamraju

Severine Rosat
Akinori Saito
Tatsuhiko Saito
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Hisayoshi Shimizu
Wataru Suzuki
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Sunny Tam
Naoki Uchida
Yanbin Wang
Yih-Min Wu
Chuang Xuan
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Yuhji Yamamoto
Tadashi Yamasaki
Yusuke Yokota
Yohei Yukutake
Seiji Zenitani

Hiroo Kanamori
Jun'ichiro Kawaguchi
Takafumi Matsui
Hitoshi Mizutani

Yasuo Ogawa
Toshitaka Tsuda
Zhongliang Wu
Kiyoshi Yomogida

Advisory Board
Benjamin Fong Chao
Bernard Chouet
Yoshimori Honkura
Toshihiko Iyemori

Journal Scope
Earth, Planets and Space (EPS) is the official journal of Society of Geomagnetism and Earth, Planetary
and Space Sciences, The Seismological Society of Japan, The Volcanological Society of Japan, The
Geodetic Society of Japan, and The Japanese Society for Planetary Sciences.
EPS is a peer-reviewed, open-access journal published under SpringerOpen. It is an international journal
covering scientific articles in the entire field of earth and planetary sciences, particularly geomagnetism,aeronomy, space science, seismology, volcanology, geodesy, and planetary science. EPS also welcomesarticles in new and interdisciplinary subjects, and technical reports on instrumentation and software.
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Earth, Planets and Space(2021) 73:83
Stolle et al. Earth, Planets and Space
https://doi.org/10.1186/s40623-021-01409-0

Open Access

PREFACESpecial issue “Characterizationof the geomagnetic field and its dynamic
environment using data from space-basedmagnetometers”
C. Stolle1,2*, N. Olsen3, B. Anderson4, E. Doornbos5 and A. Kuvshinov6

on a boom, but those missions often neither measure
the absolute magnetic field intensity together with thevariations of the magnetic components nor provide precise attitude determination of the magnetometer itself.
However, magnetic data from these missions have beenshown to add valuable information in characterizing thegeomagnetic field and its environment after appropriate
calibration.
This special issue collects articles that document successful calibration strategies including the validation of
their results, e.g., by comparison to other data or appliedin exemplary science cases, and articles that outline valuable research application in Earth and space sciences by
the use of these magnetometer data. Figure 1 shows thealtitude distribution of the satellite missions, which data
were analyzed in papers of this special issue. In combination, they provide a multi-mission data set in LEO spanning almost two solar cycles.
Extending the calibration scheme developed andapplied to data from high-precision satellite missions,
Olsen et al. (2020) introduce an approach for characterization, calibration, and alignment of vector magnetometer data, applied to data from the platform
magnetometers onboard ESA’s CryoSat-2 satellite. The
calibration is performed by comparing the magnetometer sensor readings with magnetic field values for thetime and position of the satellite as given by an a priori
high-precision geomagnetic field model, e.g. CHAOS(Finlay et al. 2020), to estimate the magnetometer calibration parameters by solving a least square problem.
The calibrated magnetic data show good agreement with

The main part of the geomagnetic field arises from electric currents in the Earth’s outer core. It extends to a
distance of ∼ 10 Earth radii and acts as a shield for protecting our atmosphere against solar and cosmic particle
radiation. It also determines the strength and geometry ofionospheric and magnetospheric current systems. While
the Earth’s core field varies on time scales of months toyears, electric currents in the ionosphere and magnetosphere change within seconds to days, e.g., during space
weather events. Continuous monitoring of the various
magnetic field variations is thus important to characterize the Earth’s space environment and ensure the preparedness of modern technology on the ground and in spaceon which society increasingly depends.
Most of our knowledge of the spatial and temporal variations of the recent geomagnetic field has been obtainedusing observations taken by high precision magnetic satellite missions, such as Ørsted, CHAMP, and currently
the European Space Agency’s (ESA) magnetic field constellation mission Swarm. However, a multitude of satellites in low Earth orbit (LEO) carry magnetometers that,by design, do not meet the accuracy of dedicated geomagnetic missions. These are avionic, so-called platform
magnetometers that are primarily used for coarse attitude determination of the spacecraft. Another category ismagnetometers meant for science applications mounted*Correspondence: cstolle@gfz-potsdam.de1Helmholtz Centre Potsdam, GFZ German Research Centre
for Geosciences, Telegrafenberg, 14473 Potsdam, Germany
Full list of author information is available at the end of the article© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing,
adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) andthe source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material
in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material
is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds thepermitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativeco
mmons.org/licenses/by/4.0/.

1Characterization of the Geomagnetic Field and Its Dynamic Environment Using Data from Space-Based Magnetometers
Stolle et al. Earth, Planets and Space(2021) 73:83

Page 2 of 4

Fig. 1 Altitude of satellite missions used in this special issue (left scale) and solar flux index F10.7 (right scale). Altitude of high-precision magnetic
missions are plotted by thinner lines, those of others by bolder lines. Altitudes between 26 July 2000 and 24 January 2021 are shown. Ørsted
altitudes are shown up to 12/2005 until the mission provided high-precision magnetic datawith a model of Earth’s magnetic field. This method does
not require an a priori geomagnetic field model such as
CHAOS but relies on supporting calibrated magnetic
data, here provided by CHAMP, Swarm, and groundobservatories. The authors apply this scheme to calibratemagnetic data from the DMSP and CryoSat-2 missions
to enhance the description of the rapid core field evolution when satellite-based high-precision magnetic data
were not available, e.g., during the gap period between
CHAMP and Swarm in 2010–2013 (see Fig. 1).
Kloss et al. (2021) present a similar approach, go further, and co-estimate both the internal (core) and theexternal (magnetospheric) part of geomagnetic fieldmodels along with magnetometer calibration parameters.
By that, they derive a geomagnetic field model spanning2008 to 2018 with satellite magnetic data from CHAMP,
Swarm, data from ground observatories, and platform
magnetometer data from CryoSat-2 and the GRACE
satellite pair. It was proven that platform magnetometerdata provide additional information on the secular acceleration, especially in the Pacific Ocean region during the
gap between CHAMP and Swarm.
Hammer et al. (2021) use time series of geomagnetic
secular variation at 300 globally distributed geomagnetic virtual observatories to study time variations of the
Earth’s core magnetic field both at satellite altitude andat the core–mantle boundary. They use 20 years of continuous magnetic field measurements from the Ørsted,
CHAMP, and Swarm satellite missions and calibrated
platform magnetometer data from the CryoSat-2 satellite.
The authors find that CryoSat-2 platform magnetometerdata provide a valuable contribution to emerging picturesof regional sub-decadal core field variations.
Velímský and Knopp (2021) and Kuvshinov et al.
(2021) use up to 6 years of contemporaneous magnetic
observations of Swarm and CryoSat-2 to determine the

Swarm satellite magnetic measurements during close
encounters. Furthermore, it was demonstrated that the
CryoSat-2 magnetic variations follow well the Dst-index
during a geomagnetic storm event.
Stolle et al. (2021) applied a similar least-square fit toplatform magnetometer data of the GRACE-FO dualsatellite constellation mission. The average mean of theremaining residuals to the CHAOS model used in thecalibration process show standard deviations below
10 nT rms, which are similar to those derived for CryoSat-2. By combining the Swarm, GRACE-FO, and CryoSat-2 satellites, the authors showed that the extended“constellation” does well capture the local time evolutionof the magnetospheric ring current under geomagnetic
storm conditions. Also, GRACE-FO-derived auroral
field-aligned currents compare well in amplitude withthose derived from Swarm data. The pearls-on-a-string
configuration of the GRACE-FO mission further allows
scale analyses of ionospheric structures.
Olsen (2021) extended the scheme to process and calibrate the platform magnetometer data of the GRACE
dual-satellite mission. The remaining residuals to themodels are somewhat higher than those for CryoSat-2
and GRACE-FO due to lacking direct measurements ofmagnetometer temperature and the rather coarse 12-bit
discretization of the GRACE magnetometers; however,the data have been proven relevant for geophysical applications in publications mentioned below. Besides, by
combining data from the Swarm, GRACE, and CryoSat-2
satellites in spherical harmonic (SH) analyses, the author
confirms that the local time asymmetric part of the magnetospheric ring current after the peak of a geomagnetic
storm decays faster compared to its symmetric part.
Alken et al. (2020) provide the Frontier Letter for thisspecial issue. They describe a novel scheme for co-estimating magnetometer calibration parameters together

2Earth, Planets and Space
Stolle et al. Earth, Planets and Space(2021) 73:83

Page 3 of 4of the currents is systematic southward throughout theyear in the South Atlantic sector due to the predominantgeometry and relatively low strength of the magnetic
field in that region. The paper provides observational evidences of noontime dynamo currents at the highest altitude (of about 700 km, sampled by CryoSat-2) reported
so far.
In conclusion, appropriately calibrated data from nondedicated magnetometers onboard LEO satellites havehigh value for both Earth’s and space research. Examples
include (1) filling periods of unavailability of high-precision data, (2) the combination of several missions to a“constellation” for better spatio-temporal coverage, and(3) the availability of geomagnetic observations at multiple platforms, which provides an extended opportunity
to perform combined analysis with other ionosphericparameters sampled by particular missions. It is nonetheless noteworthy that these magnetic data have been calibrated along with high-precision observations or using
high-resolution geomagnetic field models derived frommeasurements by the Swarm satellites. Simultaneous
data from at least one dedicated high-precision magnetic
satellite mission thus remain crucial for this endeavor.

three-dimensional (3-D) structure of mantle conductivity. The largest benefit from combining the missions was
through the enhanced coverage of local time sectors at
same observational periods. In their works, the teams followed different approaches.
Velímský and Knopp (2021) perform time-domain
forward and inverse electromagnetic (EM) induction
modeling to the latest version of satellite-derived timeseries of SH coefficients of external (inducing) and internal (induced) parts of the magnetic potential describing signals of magnetospheric origin. The inclusion of
CryoSat-2 platform magnetometer data had only small
influence on the inversion results, but allow for a larger
reduction of the data misfit in the applied inversion. The
authors recovered large-scale conductivity structures(parameterized by SH up to degree 3) in Earth’s mantle,
which partially overlap with the shape of the large lowshear velocity provinces in the lower mantle.
Kuvshinov et al. (2021) rely on the estimation andinversion of the so-called matrix Q-responses, which
relate in the frequency domain the SH coefficients of
inducing and induced parts of the magnetic potential.
Their results show a significant deviation of mantle conductivity distribution from the global 1-D conductivity
profile in the Pacific Ocean region. In their outlook, theauthors emphasized the need for the data from more andbetter distributed (in terms of local time coverage) satellite missions; this will allow for an improved descriptionof the source geometry in the ionosphere and magnetosphere, the prerequisite for future advances in global 3-D
EM mapping of mantle conductivity.
Looking at studies of ionospheric current systems,
Xiong et al. (2020) compare auroral field-aligned currents(FAC) derived from magnetic data of the DMSP mission
with simultaneous energetic particle fluxes detected at
the same spacecraft. They performed the first statistical study of these parameters’ relation from simultaneous data and found systematic differences in the locationof peaks of particle energy flux and large-scale FACs,
emphasizing the complexity of the auroral oval region.
Furthermore, during conjunction events, the DMSP
field-aligned currents were proven to be similar in amplitude with Swarm-derived results further supporting theirvalue for space science.
Park et al. (2020) demonstrate that calibrated platform
magnetic data can also be used in statistical investigations of low amplitude ionospheric currents at non-polar
latitudes. From vertical currents detected during 8 years
at CryoSat-2 and during nearly 2 years at GRACE-FO theauthors successfully derive global pattern of interhemispheric FACs, the distribution of which is dominatedby seasonal variations and tidal forcing from the lower
atmosphere. They further discussed that the direction

Abbreviations
CHAMP: CHAllenging Minisatellite Payload; CHAOS: CHAmp Ørsted SAC-C
magnetic field model; DMSP: Defense Meteorological Satellite Program; Dst:
Geomagnetic Equatorial Disturbance Storm Time Index; EM: Electromagnetic;
ESA: European Space Agency; FAC: Field-Aligned Currents; GRACE(-FO):
Gravity Recovery and Climate Experiment (-Follow-On); LEO: Low Earth Orbit;
rms: Root Mean Square; SH: Spherical Harmonic; 1-D: One-dimensional; 3-D:
Three-dimensional.
Acknowledgements
We express our sincere gratitude to the authors who contributed to thisspecial issue and the reviewers who evaluated the contributions and gavethoughtful comments and suggestions. We also thank Editors-in-Chief Yasuo
Ogawa and Takeshi Sagiya for their support and the various institutions andentities that operate satellites and provide data.
Authors’ contributions
All authors of this article served as guest editors for this special issue. All
authors read and approved the final manuscript.
Funding
This initiative has been partly supported by Swarm DISC activities funded by
ESA under contract no. 4000109587/13/I-NB.

Declarations
Competing interests
The authors declare that they have no competing interests.
Author details
1
Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences,
Telegrafenberg, 14473 Potsdam, Germany. 2 Faculty of Science, Universityof Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany. 3 Divisionof Geomagnetism and Geospace, DTU Space, Technical University of Denmark, Centrifugevej 356, 2800 Kongens Lyngby, Denmark. 4 Applied Physics
Laboratory, Johns Hopkins University, 11100 Johns Hopkins Rd, Laurel, MD,
USA. 5 Royal Netherlands Meteorological Institute (KNMI), Utrechtseweg 297,3

Characterization of the Geomagnetic Field and Its Dynamic Environment Using Data from Space-Based Magnetometers
Stolle et al. Earth, Planets and Space(2021) 73:83

Page 4 of 4

3731 GA De Bilt, The Netherlands. 6 Institute of Geophysics, ETH Zürich, Sonneggstrasse, 8092 Zurich, Switzerland.

Olsen N (2021) Magnetometer data from the GRACE satellite duo. Earth Planets Space 73. https://doi.org/10.1186/s40623-021-01373-9
Olsen N, Albini G, Bouffard J, Parrinello T, Tøffner-Clausen L (2020) Magnetic
observations from CryoSat-2: calibration and processing of satellite
platform magnetometer data. Earth Planets Space 72:48. https://doi.org/
10.1186/s40623-020-01171-9.
Park J, Stolle C, Yamazaki Y, Rauberg J, Michaelis I, Olsen N (2020) Diagnosing
low-/mid-latitude ionospheric currents using platform magnetometers:
CryoSat-2 and GRACE-FO. Earth Planets Space 72. https://doi.org/10.
1186/s40623-020-01274-3
Stolle C, Michaelis I, Xiong C, Rother M, Usbeck T, Yamazaki Y, Rauberg J,
Styp-Rekowski K (2021) Observing Earth’s magnetic environment with
the GRACE-FO mission. Earth Planets Space 73. https://doi.org/10.1186/
s40623-021-01364-w
Velímský J, Knopp O (2021) Lateral variations of electrical conductivity in thelower mantle constrained by Swarm and CryoSat-2 missions. Earth Planets Space 73. https://doi.org/10.1186/s40623-020-01334-8
Xiong C, Stolle C, Alken P, Rauberg J (2020) Relationship between large-scale
ionospheric field-aligned currents and electron/ion precipitations:DMSP observations. Earth Planets Space 72. https://doi.org/10.1186/
s40623-020-01286-z

Received: 25 March 2021 Accepted: 26 March 2021

References
Alken P, Olsen N, Finlay C (2020) Co-estimation of geomagnetic field and inorbit fluxgate magnetometer calibration parameters. Earth Planets Space72. https://doi.org/10.1186/s40623-020-01163-9
Finlay C, Kloss C, Olsen N, M H, Tøffner-Clausen L, Grayver A, Kuvshinov A(2020) The CHAOS-7 geomagnetic field model and observed changes in
the South Atlantic Anomaly. Earth Planets Space 72. https://doi.org/10.
1186/s40623-020-01252-9
Hammer MD, Finlay CC, Olsen N (2021) Applications of CryoSat-2 satellite
magnetic data in studies of the Earth’s core field variations. Earth Planets
Space 73. https://doi.org/10.1186/s40623-021-01365-9
Kloss C, Finlay CC, Olsen N (2021) Co-estimating geomagnetic field andcalibration parameters: modeling Earth’s magnetic field with platform
magnetometer data. Earth Planets Space 73. https://doi.org/10.1186/
s40623-020-01351-7
Kuvshinov A, Grayver A, Tøffner-Clausen L, Olsen N (2021) Probing 3-D electrical conductivity of the mantle using 6 years of Swarm, CryoSat-2 andobservatory magnetic data and exploiting matrix Q-responses approach.
Earth Planets Space 73. https://doi.org/10.1186/s40623-020-01341-9

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

4Earth, Planets and SpaceFRONTIER LETTER

Open AccessCo-estimation of geomagnetic field and in-orbit fluxgate
magnetometer calibration parameters
Patrick Alken*, Nils Olsen and Christopher C. Finlay
Earth, Planets and Space 2020, 72:49 DOI: 10.1186/s40623-020-01163-9
Received: 14 December 2019, Accepted: 12 March 2020, Published: 14 April 2020

Abstract
For the past 20 years, state of the art geomagnetic core field models have relied heavily on magnetic measurements made from space-based
instrumentation. These models have revealed rapid global magnetic field variations on sub-decadal timescales originating in Earth’s core. With
the end of the CHAMP mission in 2010 and the launch of Swarm in late 2013, there has been a 3-year gap
in high-quality satellite measurements of the geomagnetic field. Geomagnetic field models havetherefore relied on ground observatory data to fill in this gap period. However, ground observatories areunable to provide a truly global picture of the core field and its temporal changes. Many satellites inoperation carry vector fluxgate “platform” magnetometers for attitude control, which can offer analternative to relying on ground observatory measurements during the gap period. However, these
instruments need to be carefully calibrated in order to provide meaningful information on Earth’s core
field. Some previous studies attempted to calibrate such instruments with a priori geomagnetic fieldmodels. This approach has several disadvantages: (1) errors in the model will introduce errors in thecalibration parameters, and (2) relying on an a priori model may not be feasible in the post-Swarm era. In
this paper, we develop a novel approach to build a time-dependent geomagnetic field model fromplatform magnetometer data, by co-estimating their calibration parameters with the internal fieldparameters. This method does not require an a priori geomagnetic field model, but does require a datasetof previously calibrated data. We use CHAMP, Swarm, and ground observatory measurements to supply
this dataset, and incorporate platform magnetic measurements from DMSP and Cryosat-2 during the gap
years. We find that the calibration parameters of DMSP and Cryosat-2 can be reliably estimated, and thesemissions provide meaningful information on rapid core field variations during the gap period.

Keywords: Geomagnetism, Core field modeling, Secular variation, Secular acceleration, Fluxgate
calibration, Inverse theory

Graphical abstract*Corresponding author: Patrick Alken, alken@colorado.edu

FULL PAPER

Open Access

Magnetic observations from CryoSat-2: calibration andprocessing of satellite platform magnetometer data
Nils Olsen*, Giuseppe Albini, Jerome Bouffard, Tommaso Parrinello and Lars Tøffner-Clausen
Earth, Planets and Space 2020, 72:48 DOI: 10.1186/s40623-020-01171-9
Received: 5 December 2019, Accepted: 22 March 2020, Published: 9 April 2020

Abstract
We describe and discuss the preprocessing and calibration steps applied to the magnetic data measured by the three “platform
magnetometers” on-board the CryoSat-2 satellite. The calibration is performed by comparing the magnetometer sensor readings
with magnetic field values for the time and position of the satellite as given by the CHAOS-6 geomagnetic field model. We allow
for slow temporal variations of the calibration parameters by solving for scale values, offsets, and non-orthogonalities in monthly
bins, and account for non-linearities as well as the magnetic disturbances caused by battery, solar panel and magnetorquer
currents. Fully calibrated magnetic vector data, together with timeand position, are provided as daily files in CDF data format at
swarm-diss.eo.esa.int. The data show good agreement with Swarmsatellite magnetic measurements during close encounters (rms
difference between 1 and 5 nT for inter-satellite distances below
300 km).

Keywords: Geomagnetism, Magnetic satellites, Magnetometer
calibration, CryoSat-2

Graphical abstract*Corresponding author: Nils Olsen, nio@space.dtu.dk
5Characterization of the Geomagnetic Field and Its Dynamic Environment Using Data from Space-Based Magnetometers

FULL PAPER

Open Access

Relationship between large-scale ionospheric field-aligned
currents and electron/ion precipitations: DMSP observations
Chao Xiong*, Claudia Stolle, Patrick Alken and Jan Rauberg
Earth, Planets and Space 2020, 72:147 DOI: 10.1186/s40623-020-01286-z
Received: 30 May 2020, Accepted: 30 September 2020, Published: 16 October 2020

Abstract
In this study, we have derived field-aligned currents (FACs) from magnetometers onboard the Defense Meteorological Satellite Project(DMSP) satellites. The magnetic latitude versus local time distribution of FACs from DMSP shows comparable dependences with previous
findings on the intensity and orientation of interplanetary magnetic field (IMF) By and Bz components, which confirms the reliability of
DMSP FAC data set. With simultaneous measurements of precipitating particles from DMSP, we further investigate the relation between
large-scale FACs and precipitating particles. Our result shows that precipitation electron and ion fluxes both increase in magnitude andextend to lower latitude for enhanced southward IMF Bz, which is similar to the behavior of FACs. Under weak northward and southward
Bz conditions, the locations of the R2 current maxima, at both dusk and dawn sides and in both hemispheres, are found to be close to the
maxima of the particle energy fluxes; while for the same IMF conditions, R1 currents are displaced further to the respective particle flux
peaks. Largest displacement (about 3.5°) is found between the
downward R1 current and ion flux peak at the dawn side. Our results
suggest that there exists systematic differences in locations of electron/
ion precipitation and large-scale upward/downward FACs. As outlinedby the statistical mean of these two parameters, the FAC peaks enclose
the particle energy flux peaks in an auroral band at both dusk anddawn sides. Our comparisons also found that particle precipitation at
dawn and dusk and in both hemispheres maximizes near the mean R2
current peaks. The particle precipitation flux maxima closer to the R1
current peaks are lower in magnitude. This is opposite to the known
feature that R1 currents are on average stronger than R2 currents.

Keywords: Field-aligned currents, Aurora, Particle precipitation,
DMSP

Graphical abstract*Corresponding author: Chao Xiong, bear@gfz-potsdam.de

FULL PAPER

Open Access

Diagnosing low-/mid-latitude ionospheric currents using
platform magnetometers: CryoSat-2 and GRACE-FO
Jaeheung Park*, Claudia Stolle, Yosuke Yamazaki, Jan Rauberg, Ingo Michaelis and Nils Olsen
Earth, Planets and Space 2020, 72:162 DOI: 10.1186/s40623-020-01274-3
Received: 8 July 2020, Accepted: 15 September 2020, Published: 27 October 2020

Abstract
Electric currents flowing in the terrestrial ionosphere have conventionally been diagnosed by low-earth-orbit (LEO) satellites equipped with
science-grade magnetometers and long booms on magnetically clean satellites. In recent years, there are a variety of endeavors to incorporate
platform magnetometers, which are initially designed for navigation purposes, to study ionospheric currents. Because of the suboptimal
resolution and significant noise of the platform magnetometers, however, most of the studies were confined to high-latitude auroral regions,where magnetic field deflections from ionospheric currents easily exceed 100 nT. This
study aims to demonstrate the possibility of diagnosing weak low-/mid-latitude
ionospheric currents based on platform magnetometers. We use navigation
magnetometer data from two satellites, CryoSat-2 and the Gravity Recovery andClimate Experiment Follow-On (GRACE-FO), both of which have been intensively
calibrated based on housekeeping data and a high-precision geomagnetic fieldmodel. Analyses based on 8 years of CryoSat-2 data as well as ~ 1.5 years of GRACE-FO
data reproduce well-known climatology of inter-hemispheric field-aligned currents(IHFACs), as reported by previous satellite missions dedicated to precise magnetic
observations. Also, our results show that C-shaped structures appearing in noontime
IHFAC distributions conform to the shape of the South Atlantic Anomaly. The F-region
dynamo currents are only partially identified in the platform magnetometer data,
possibly because the currents are weaker than IHFACs in general and depend
significantly on altitude and solar activity. Still, this study evidences noontime
F-region dynamo currents at the highest altitude (717 km) ever reported. We expectthat further data accumulation from continuously operating missions may reveal the
dynamo currents more clearly during the next solar maximum.

Keywords: Platform magnetometers, CryoSat-2, GRACE-FO, Inter-hemisphericfield-aligned currents, F-region dynamo currents*Corresponding author: Jaeheung Park, pj@kasi.re.kr
6

Graphical abstract

Earth, Planets and Space

FULL PAPER

Open Access

Lateral variations of electrical conductivity in the lower
mantle constrained by Swarm and CryoSat-2 missions
Jakub Velímský* and Ondřej Knopp
Earth, Planets and Space 2021, 73:4 DOI: 10.1186/s40623-020-01334-8
Received: 19 October 2020, Accepted: 6 December 2020, Published: 4 January 2021

Abstract
The electrical conductivity is an important geophysical parameter connected to the thermal, chemical, and mineralogical state of
the Earth’s mantle. In this paper, we apply the previously developed methodology of forward and inverse EM induction modelingto the latest version of satellite-derived spherical harmonic coefficients of external and internal magnetic field, and obtain thefirst 3-D mantle conductivity models with contributions from Swarm and CryoSat-2 satellite data. We recover degree 3
conductivity structures which partially overlap with the shape of the large low-shear velocity provinces in the lower mantle.

Keywords: EM induction, Mantle electrical conductivity, Swarm, CryoSat-2
670 km - 900 km

-1

-0.5

0

0.5

1

Graphicallog ( σ inabstract
S/m)*Corresponding author: Jakub Velímský, jakub.velimsky@mf.cuni.cz

FULL PAPER

Open AccessCo-estimating geomagnetic field and calibration parameters:
modeling Earth’s magnetic field with platform
magnetometer data
Clemens Kloss*, Christopher C. Finlay and Nils Olsen
Earth, Planets and Space 2021, 73:23 DOI: 10.1186/s40623-020-01351-7
Received: 30 September 2020, Accepted: 26 December 2020, Published: 20 January 2021

Abstract
Models of the geomagnetic field rely on magnetic data of high spatial and temporal resolution to give an accurate picture of the Earth’s internal
magnetic field and its time-dependence. The magnetic data from low-Earth orbit satellites of dedicated magnetic survey missions such as
CHAMP and Swarm play a key role in the construction of such models. Unfortunately, there are no magnetic data available from such satellites
after the end of the CHAMP mission in 2010 and before the launch of the Swarm mission in late 2013. This limits our ability to recover signals ontimescales of 3 years and less during this gap period. The magnetic data from platform magnetometers carried by satellites for navigational
purposes may help address this data gap provided that they are carefully calibrated. Earlier studies have demonstrated that platform
magnetometer data can be calibrated using a fixed geomagnetic field model as reference. However, this approach can lead to biased calibration
parameters. An alternative approach has been developed in the form of a co-estimation scheme which consists of simultaneously estimating
both the calibration parameters and a model of the internal part of the geomagnetic field. Here, we go further and develop a scheme, based on
the CHAOS field modeling framework, that involves co-estimation of both internal and external geomagnetic field models along with calibration
parameters of platform magnetometer data. Using our implementation, we are able to derive a geomagnetic field model spanning 2008 to 2018with satellite magnetic data from CHAMP, Swarm, secular variation data from ground observatories, and platform magnetometer data fromCryoSat-2 and the GRACE satellite pair. Through a number of experiments, we
explore correlations between the estimates of the geomagnetic field and thecalibration parameters, and suggest how these may be avoided. We findevidence that platform magnetometer data provide additional information on
the secular acceleration, especially in the Pacific during the gap between
CHAMP and Swarm. This study adds to the evidence that it is beneficial to use
platform magnetometer data in geomagnetic field modeling.

Keywords: Geomagnetism, Core field modeling, Inverse theory, Secular
acceleration, Secular variation*Corresponding author: Clemens Kloss, ancklo@space.dtu.dk
7Graphical abstract

Characterization of the Geomagnetic Field and Its Dynamic Environment Using Data from Space-Based Magnetometers

FULL PAPER

Open AccessObserving Earth’s magnetic environment with
the GRACE-FO mission
C. Stolle*, I. Michaelis, C. Xiong, M. Rother, Th. Usbeck, Y. Yamazaki, J. Rauberg and K. Styp-Rekowski
Earth, Planets and Space 2021, 73:51 DOI: 10.1186/s40623-021-01364-w
Received: 15 September 2020, Accepted: 18 January 2021, Published: 15 February 2021

Abstract
The Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) mission carries magnetometers that are dedicated to enhance the satellite’snavigation. After appropriate calibration and characterisation of artificial magnetic disturbances, these observations are valuable assets tocharacterise the natural variability of Earth’s magnetic field. We describe the data pre-processing, the calibration, and characterisation strategy
against a high-precision magnetic field model applied to the GRACE-FO magnetic data. During times of geomagnetic quiet conditions, the mean
residual to the magnetic model is around 1 nT with standard deviations below 10 nT. The mean difference to data of ESA’s Swarm mission, which
is dedicated to monitor the Earth’s magnetic field, is mainly within ± 10 nT during conjunctions. The performance of GRACE-FO magnetic data isfurther discussed on selected scientific examples. During a magnetic storm event in August 2018, GRACE-FO reveals the local time dependenceof the magnetospheric ring current signature, which is in good agreement with results from a network of ground magnetic observations. Also,
derived field-aligned currents (FACs) are applied to monitor auroral FACs that compare well in amplitude and statistical behaviour for local time,hemisphere, and solar wind conditions to approved earlier findings from other missions including Swarm. On a case event, it is demonstrated
that the dual-satellite constellation of GRACE-FO is most suitable toderive the persistence of auroral FACs with scale lengths of 180 km
or longer. Due to a relatively larger noise level compared to
dedicated magnetic missions, GRACE-FO is especially suitable forhigh-amplitude event studies. However, GRACE-FO is also sensitive
to ionospheric signatures even below the noise level within
statistical approaches. The combination with data of dedicatedmagnetic field missions and other missions carrying nondedicated magnetometers greatly enhances related scientificperspectives.

Keywords: Earth’s magnetic field, Geomagnetism, Ionosphericcurrents, Magnetospheric ring current, Satellite-basedmagnetometers, Platform magnetometers, GRACE-FO

Graphical abstract*Corresponding author: C. Stolle, cstolle@gfz‑potsdam.de

FULL PAPER

Open Access

Magnetometer data from the GRACE satellite duo
Nils Olsen
Earth, Planets and Space 2021, 73:62 DOI: 10.1186/s40623-021-01373-9
Received: 5 October 2020, Accepted: 29 January 2021, Published: 3 March 2021

Abstract
This paper describes and discusses the preprocessing and calibration of the magnetic data taken by the navigational
magnetometers onboard the two GRACE satellites, with focus on the almost 10 years period from January 2008 to the end of the
GRACE mission in October 2017 for which 1-Hz magnetic data are available. A calibration of the magnetic data is performed bycomparing the raw magnetometer sensor readings with model magnetic vector values as provided by the CHAOS-7
geomagnetic field model for the time and position of the GRACE data. The presented approach also accounts for magnetic
disturbances produced by the satellite’s magnetorquer and for temperature effects, which are parametrized by the Sun incident
angle. The root-mean-squared error of the difference between
the calibrated data and CHAOS-7 model values is about 10 nT,
which makes the GRACE magnetometer data relevant for
geophysical investigations.

Keywords: Geomagnetism, Magnetic satellites,

Magnetometer calibration, GRACE satellites

Graphical abstract

Corresponding author: Nils Olsen, nio@space.dtu.dk
8

Earth, Planets and Space

FULL PAPER

Open Access

Probing 3-D electrical conductivity of the mantle using
6 years of Swarm, CryoSat-2 and observatory magnetic
data and exploiting matrix Q-responses approach
Alexey Kuvshinov*, Alexander Grayver, Lars Tøffner-Clausen and Nils Olsen
Earth, Planets and Space 2021, 73:67 DOI: 10.1186/s40623-020-01341-9
Received: 13 October 2020, Accepted: 15 December 2020, Published: 9 March 2021

Abstract
This study presents results of mapping three-dimensional (3-D) variations of the electrical conductivity in depths ranging from
400 to 1200 km using 6 years of magnetic data from the Swarm and CryoSat-2 satellites as well as from ground observatories.
The approach involves the 3-D inversion of matrix Q-responses (transfer
410 km - 670 km
functions) that relate spherical harmonic coefficients of external (inducing) andinternal (induced) origin of the magnetic potential. Transfer functions were
estimated from geomagnetic field variations at periods ranging from 2 to 40
days. We study the effect of different combinations of input data sets on the
670 km - 900 km
transfer functions. We also present a new global 1-D conductivity profile basedon a joint analysis of satellite tidal signals and global magnetospheric
Q-responses.

Keywords: Electromagnetic induction, Three-dimensional conductivity

models, Matrix Q-responses, Inversion, Time-varying magnetic
field, Magnetosphericring-current source, Satellite data, Observatory data

900 km - 1200 km

-1

0

1

Graphical abstract*Corresponding author: Alexey Kuvshinov, kuvshinov@erdw.ethz.ch

FULL PAPER

Open Access

Applications for CryoSat-2 satellite magnetic data instudies of Earth’s core field variations
Magnus D. Hammer*, Christopher C. Finlay and Nils Olsen
Earth, Planets and Space 2021, 73:73 DOI: 10.1186/s40623-021-01365-9
Received: 5 October 2020, Accepted: 20 January 2021, Published: 18 March 2021

Abstract
We use 20 years of continuous magnetic field measurements from the Ørsted, CHAMP and Swarm satellite missions, supplemented by calibrated
platform magnetometer data from the CryoSat-2 satellite, to study time variations of the Earth’s core field at satellite altitude and at the core–mantle
boundary (CMB). From the satellite data we derive composite time series of the core field secular variation (SV) with 4-month cadence, at 300 globally
distributed Geomagnetic Virtual Observatories (GVO). A previous gap in the GVO series between 2010 and 2014 is successfully filled using CryoSat-2,
and sub-decadal variations are identified during this period. Tests showed that similar sub-decadal SV patterns were obtained from the CryoSat-2 data
regardless of whether IGRF-13 or CHAOS-6x9 was used in their calibration. Cryosat-2 radial field SV series at non-polar latitudes have a mean standard
deviation level compared to smoothing spline fits of 3.5 nT/yr compared to 1.8 nT/yr for CHAMP and 0.9 nT/yr for Swarm. GVO radial SV series display
regional fluctuations with 5–10 years duration and amplitudes reaching 20 nT/yr, most notably at low latitudes over Indonesia (2014), over SouthAmerica and the South Atlantic (2007, 2011 and 2014), and over the central Pacific (2017). Applying
the Subtractive Optimally Localized Averages (SOLA) method, we also map the radial SV at the CMB
as a collection of locally averaged SV estimates. We demonstrate that using 2-year windows of
CryoSat-2 data, it is possible to reliably estimate the SV and its time derivative, the secular
acceleration (SA), at the CMB, with a spatial resolution, corresponding to spherical harmonic degree
10. Along the CMB geographic equator, we find strong SA features with amplitude ±2.5 μT/yr2 underIndonesia from 2011–2014, under central America from 2015 to 2019, and sequences of SA withalternating sign under the Atlantic during 2004–2019. We find that platform magnetometer datafrom CryoSat-2 make a valuable contribution to the emerging picture of sub-decadal core field
variations. Using 1-year windows of data from the Swarm satellites, we show that it is possible tostudy SA changes at low latitudes on timescales down to 1 year, with spatial resolution
corresponding to spherical harmonic degree 10. We find strong positive and negative SA featuresappearing side-by-side in the Pacific in 2017, and thereafter drift westward.

Keywords: Geomagnetism, Secular variation, Secular acceleration, Earth’s core, Platform
magnetometer, CryoSat-2 satellite Swarm satellite constellation*Corresponding author: Magnus D. Hammer, magdh@space.dtu.dk
9Graphical abstract

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Contents
Special issue “Characterization of the geomagnetic field and its dynamic environment using data from space-basedmagnetometers”........................................................................................ C. Stolle, N. Olsen, B. Anderson, E. Doornbos and A. Kuvshinov
Co-estimation of geomagnetic field and in-orbit fluxgate magnetometer calibration parameters............................................................................................................................................... Patrick Alken, Nils Olsen and Christopher C. Finlay
Magnetic observations from CryoSat-2: calibration and processing of satellite platform magnetometer data..................................................................... Nils Olsen, Giuseppe Albini, Jerome Bouffard, Tommaso Parrinello and Lars Tøffner-Clausen
Relationship between large-scale ionospheric field-aligned currents and electron/ion precipitations: DMSP observations................................................................................................................................ Chao Xiong, Claudia Stolle, Patrick Alken and Jan Rauberg
Diagnosing low-/mid-latitude ionospheric currents using platform magnetometers: CryoSat-2 and GRACE-FO.................................................................... Jaeheung Park, Claudia Stolle, Yosuke Yamazaki, Jan Rauberg, Ingo Michaelis and Nils Olsen
Lateral variations of electrical conductivity in the lower mantle constrained by Swarm and CryoSat-2 missions.......................................................................................................................................................................... Jakub Velímský and Ondřej Knopp
Co-estimating geomagnetic field and calibration parameters: modeling Earth’s magnetic field with platform
magnetometer data.................................................................................................... Clemens Kloss, Christopher C. Finlay and Nils Olsen
Observing Earth’s magnetic environment with the GRACE-FO mission.........................................................C. Stolle, I. Michaelis, C. Xiong, M. Rother, Th. Usbeck, Y. Yamazaki, J. Rauberg and K. Styp-Rekowski
Magnetometer data from the GRACE satellite duo........................................................................................................................ Nils Olsen
Probing 3-D electrical conductivity of the mantle using 6 years of Swarm, CryoSat-2 and observatory magnetic data andexploiting matrix Q-responses approach......................Alexey Kuvshinov, Alexander Grayver, Lars Tøffner-Clausen and Nils Olsen
Applications for CryoSat-2 satellite magnetic data in studies of Earth’s core field variations...................................................................................................................................Magnus D. Hammer, Christopher C. Finlay and Nils Olsen

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Cover image: Stolle, C. et al., Earth, Planets and Space 2021, 73:83 DOI: 10.1186/s40623-021-01409-0